# Effect of relativity on observers of two different inertial frames observing an event taking place very far away [duplicate]

I am new to relativity ,So please correct me If I am wrong. In the case I have mentioned, In a gravity free space, Let us assume a stationary observer and an observer moving with a velocity 'V' w.r.t to the stationary observer.

The stationary observer looks at an event taking place very far away('X') at time 't' So the moving observer's reference (the event is taking place far away for the moving observer as well) of space time can be calculated using Lorentz transformation. if 'V' is considerably small compared to speed of light, then the transformation for space will be similar to Galilean transformation, but since the distance of the event taking place is very large the time transformation will not be Galilean. ( because of the term (V*X)/C^2)

A light year being of the order 10^16 and all objects in universe being beyond this distance, does that mean an observer moving with a speed of 10 m/s will have relativistic effects in significant form recording an event like star explosion, wobbling effects, light variation etc?